Computing the inverse of a number in finite fields GF(p) or
GF(2n) is equally important for cryptographic applications. This
paper proposes a novel
scalable and unified architecture for a Montgomery inverse hardware that
operates in both GF(p) and GF(2n) fields. We adjust and modify a GF(2n)
Montgomery inverse algorithm to accommodate multi-bit shifting hardware, making
it very similar to a previously proposed GF(p) algorithm. The
architecture is intended to be scalable, which allows the hardware to compute
the inverse of long precision numbers in a repetitive way. After implementing
this unified design it was compared with other designs. The unified hardware was
found to be eight times smaller than another reconfigurable design, with
comparable performance. Even though the unified design consumes slightly more
area and it is slightly slower than the scalable inverter implementations for
GF(p) only, it is a practical solution whenever arithmetic in the two finite
fields is needed.